Let A, B, C, D be four points; Ha, Hb, Hc, Hd the orthocenters of the triangles formed with three of them; Ga, Gb, Gc, Gd the centroids; Oa, Ob, Oc, Od the circumcenters. Let G be the intersection between GaGc and GbGd; H the intersection between HaHc and HbHd; O the intersection between OaOc and ObOd. The points G, H, O are collinear and the ratio HG: GO = 2:1.